Generating Cumulative Wear-Based Indicators for Vehicular Components

ABSTRACT

Methods, systems, and computer program products for generating wear-based indicators are provided herein. A method includes assigning a failure label to each data point associated with a component associated with a failure-caused component replacement within a pre-specified number of runtime hours of the failure-caused component replacement; assigning a non-failure label to each data point associated with a failure-caused component replacement and not within the pre-specified number of runtime hours; assigning a non-failure label to each data point associated with a scheduled component replacement; assigning a non-failure label to each data point associated with an actively running instance of the component as yet to be replaced; estimating a failure probability for the component over a pre-specified future runtime; determining a cumulative hazard function for the component based on the failure probability; and generating a cumulative wear-based indicator for the component by executing a regression function based on the cumulative hazard function.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.14/498,686, filed Sep. 26, 2014, and incorporated by reference herein.

FIELD OF THE INVENTION

Embodiments of the invention generally relate to information technology,and, more particularly, to vehicle monitoring and maintenance

BACKGROUND

In an asset-intensive industry, the value of equipment, as a fraction ofrevenue, is commonly high. The financial impact of managing andmaintaining such equipment, therefore, can be significant in suchindustries. Existing approaches for management of high-value machinerysuch as, for example, heavy industrial vehicles, include performingperiodic maintenance according to a static pre-determined schedule.However, such approaches are based on assumptions that do not apply inmany situations.

Accordingly, a need exists for techniques to design and develop acumulative wear-based indicator of future premature vehicular componentfailures by combining different sources of data.

SUMMARY

In one aspect of the present invention, techniques for generatingcumulative wear-based indicators for vehicular components are provided.An exemplary computer-implemented method can include assigning a failureclass label to each data point, from a set of multiple data pointsderived from measurements associated with a vehicular component across afleet of multiple vehicles, that (a) is associated with (i) a scheduledvehicular component replacement or (ii) a failure-caused vehicularcomponent replacement, and (b) is within a pre-specified number ofruntime hours of (i) the scheduled vehicular component replacement or(ii) the failure-caused vehicular component replacement; assigning anon-failure class label to each data point, from the set of the multipledata points, that (a) is associated with (i) a scheduled vehicularcomponent replacement or (ii) a failure-caused vehicular componentreplacement, and (b) is not within the pre-specified number of runtimehours of (i) the scheduled vehicular component replacement or (ii) thefailure-caused vehicular component replacement; and assigning anon-failure class label to each data point, from the set of the multipledata points, that is associated with an actively running instance of thevehicular component as yet to be replaced. Further, the methodadditionally includes estimating a failure probability for the vehicularcomponent at each of the multiple data points over a pre-specifiedfuture runtime of the vehicular component based on the class labelassigned to each of the multiple data points; and determining acumulative hazard function for the vehicular component based on thefailure probability, wherein said cumulative hazard function assessesthe amount of accumulated risk that the vehicular component faced from agiven start time until the present time. Also, the method includesgenerating a cumulative wear-based indicator for the vehicular componentby executing a regression function at a given time based on (i) thecumulative hazard function, (ii) one or more selected parameters, and(iii) a determination as to whether the vehicular component (a) waspreviously replaced due to a failure, (b) was previously replaced due toa non-failure scheduled replacement, or (c) is actively running as yetto be replaced.

In another aspect of the invention, an exemplary computer-implementedmethod can include assigning a failure class label to each data point,from a set of multiple data points derived from measurements associatedwith a vehicular component across a fleet of multiple vehicles, that (a)is associated with a failure-caused vehicular component replacement, and(b) is within a pre-specified number of runtime hours of thefailure-caused vehicular component replacement; assigning a non-failureclass label to each data point, from the set of the multiple datapoints, that (a) is associated with a failure-caused vehicular componentreplacement, and (b) is not within the pre-specified number of runtimehours of the failure-caused vehicular component replacement; assigning anon-failure class label to each data point, from the set of the multipledata points, that is associated with a scheduled vehicular componentreplacement; and assigning a non-failure class label to each data point,from the set of the multiple data points, that is associated with anactively running instance of the vehicular component as yet to bereplaced. Additionally, the method includes estimating a failureprobability for the vehicular component at each of the multiple datapoints over a pre-specified future runtime of the vehicular componentbased on the class label assigned to each of the multiple data points.Further, the method additionally includes determining a cumulativehazard function for the vehicular component based on the failureprobability, wherein said cumulative hazard function assesses the amountof accumulated risk that the vehicular component has faced from a givenstart time until the present time; and generating a cumulativewear-based indicator for the vehicular component by executing aregression function at a given time based on (i) the cumulative hazardfunction, (ii) one or more selected parameters, and (iii) adetermination as to whether the vehicular component (a) was previouslyreplaced due to a failure, (b) was previously replaced due to anon-failure scheduled replacement, or (c) is actively running as yet tobe replaced.

Another aspect of the invention or elements thereof can be implementedin the form of an article of manufacture tangibly embodying computerreadable instructions which, when implemented, cause a computer to carryout a plurality of method steps, as described herein. Furthermore,another aspect of the invention or elements thereof can be implementedin the form of an apparatus including a memory and at least oneprocessor that is coupled to the memory and configured to perform notedmethod steps. Yet further, another aspect of the invention or elementsthereof can be implemented in the form of means for carrying out themethod steps described herein, or elements thereof; the means caninclude hardware module(s) or a combination of hardware and softwaremodules, wherein the software modules are stored in a tangiblecomputer-readable storage medium (or multiple such media).

These and other objects, features and advantages of the presentinvention will become apparent from the following detailed descriptionof illustrative embodiments thereof, which is to be read in connectionwith the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating system architecture, according to anexample embodiment of the invention;

FIG. 2 is a flow diagram illustrating techniques according to anembodiment of the invention;

FIG. 3 is a flow diagram illustrating techniques according to anembodiment of the invention; and

FIG. 4 is a system diagram of an exemplary computer system on which atleast one embodiment of the invention can be implemented.

DETAILED DESCRIPTION

As described herein, an aspect of the present invention includestechniques for developing a cumulative wear-based indicator for avehicular component. At least one embodiment of the invention includesobtaining a set of input time series that represents a history of sampledata points, wherein each sample data point includes a combination ofmeasurements taken from a vehicular component across a fleet ofvehicles. Such measurements can encompass component data including, forexample, total runtime hours, total fuel consumption, total loadcarried, as well as sensor and replacement event information. Utilizingsuch data, at least one embodiment of the invention includes generatinga non-decreasing (in time) lifetime cumulative wear indicator functionfor a given vehicular component that is a function of the input timeseries corresponding to that component, for use as a vehicle maintenanceplanning tool.

An aspect of the invention includes identifying and utilizing multiplecharacteristics for implementation in a cumulative wear-based indicator.For instance, such characteristics can be derived from determinationsthat a cumulative wear-based indicator should be non-decreasing, andconvex-shaped (or accelerated shape) over the component runtime.

Additionally, another aspect of the invention includes an individualizedcumulative failure probability function (that is, the probability thatthe component would fail by a given time t). By way of illustration,consider, for each individual component, a hypothetical population ofcomponents that share the same history of covariates as a givenindividual component. At least one embodiment of the invention includesdefining a cumulative distribution function of the failure time for thepopulation, referred to herein as the individualized cumulative failureprobability function for the component. In addition, the individualizedcumulative failure probability function F_(j)(t) of component j includesthe following relationship with the individualized cumulative hazardfunction H_(j)(t): F_(j)(t)=1−S_(j)(t)=1−exp(−H_(j)(t)), whereinS_(j)(t) is the individualized survival probability function (that is,the probability that the component would survive (not fail) up to agiven time t). As used herein, the individualized cumulative hazardfunction H_(j)(t) (the calculation of which is described further below)assesses the total amount of accumulated risk that the component j hasfaced from the beginning of a given timeframe until the present time.

Additionally, one or more embodiments of the invention include modellinga wear indicator for a given component using the correspondingindividualized cumulative failure probability function. That is, in oneor more embodiments of the invention, the wear indicator for a componentcan be the same as its individualized cumulative failure probabilityover a given runtime.

In connection with a runtime-based policy, a scheduled replacement timecan be selected such that the cumulative failure probability F(t_(p))optimizes an economic criterion such as, for example, minimizing theaverage maintenance cost per unit runtime. Optimizing an economiccriterion can be carried out via techniques such as taught, for example,in the U.S. Patent Application with Attorney Docket NumberARC920140045US1, entitled “Integrating Economic Considerations toDevelop a Component Replacement Policy Based on a Cumulative Wear-BasedIndicator for a Vehicular Component,” filed concurrently herewith andincorporated by reference herein in its entirety. In connection with awear indicator-based policy for scheduled replacements, a wear indicatorthreshold value can be selected for and/or applied to the individualizedcumulative failure probability functions F_(j)(t) of components. This isakin to applying a common threshold to the individualized cumulativehazard functions H_(j)(t). Note, also, that in one or more embodimentsof the invention, such individualization for a cumulative failureprobability (or cumulative hazard) enables each component to have itsown transformed time scale for the given replacement policy.

As referenced above, the individualized cumulative hazard H_(j)(t)assesses the total amount of accumulated risk that the component j hasfaced from a given start time until the present time, while the(instantaneous) hazard rate assesses the risk that a component, whichhas not yet failed, will experience a failure within a unit of runtime.Compared to using the hazard rate in designing a scheduled replacementpolicy, applying the individualized cumulative hazard H_(j)(t) carriesone or more advantages. For example, in contrast to the hazard rate, theindividualized cumulative hazard can capture the accumulated wear overthe component runtime. Also, the individualized cumulative hazard isalways increasing, whereas the hazard rate may fluctuate up and downover the runtime. Note that the characteristic of monotonicallyincreasing is necessary because the wear indicator is conceptualized asa transformed time scale.

Consider, for example, a data set that includes daily-interval samples.An example embodiment of the invention can include defining the dailyhazard h_(j)(d) on date d for component j based on the total hazardduring the daily runtime. That is, daily hazard=hazard rate×dailyruntime. Subsequently, such an example embodiment of the invention caninclude estimating the individualized cumulative hazard by summing alldaily hazards until the present time t:H_(j)(t)=Σ_(all d in{d:Meter(j,d)≦t})h_(j)(d), wherein Meter(j,d) is theaccumulated runtime hours over days up to and including date d.

Note, also, that the estimated daily hazard depends on a selection ofcovariates and the model. Also, daily hazard estimates from a desirablemodel predict component failure near the date of an actual failure time.As noted above, incorrect predictions or premature predictions offailures would lead to a reduction of average runtime. Accordingly, andas additionally detailed below, at least one embodiment of the inventionincludes identifying the covariates and the model that enable the dailyhazard estimates to be convex-shaped and very close to the maximum value(that is, a value of 1) near the date of actual failure time.

In at least one embodiment of the invention, it is desired that only theindividualized cumulative hazards satisfy one or more desiredcharacteristics (such as monotonically increasing, high values of{circumflex over (t)}_(p) and {circumflex over (t)}_(f) , high wearindicator values on the failure times, etc.) for a given economiccriterion. Accordingly, such an embodiment includes designing a wearindicator model as a regression task, wherein the regression targetvariable is the designed daily hazard {tilde over (h)}_(j)(d) specifiedon any date d for component j as follows:

-   -   If the component was failure-replaced, {tilde over        (h)}_(j)(d)=(Meter(j,d)/Meter(j,T_(F)(j)))^(α), wherein        Meter(j,d) is the total runtime hours up to and including date        d, T_(F)(j) is the finally observed date (or the replacement        date), and α≧1; and    -   If the component was schedule-replaced or actively running (that        is, as yet to be replaced), {tilde over        (h)}_(j)(d)=β(Meter(j,d)/M_(max))^(α) wherein        M_(max)=max_(i)[Meter(i,T_(F)(i))]=the maximum total runtime        hours over all components in the data set, and β(<<1) is a small        positive number close to 0 (for example, β=0.1).

That is, the first equation ({tilde over(h)}_(j)(d)=(Meter(j,d)/Meter(j,T_(F)(j)))^(α)) satisfies the conditionthat failure-replaced components have the maximum value (=1) near thedate of an actual failure time, and the second equation ({tilde over(h)}_(j)(d)=β(Meter(j,d)/M_(max))^(α)) allows therunning/schedule-replaced components to have low values (that is, valuesof the designed hazard ({tilde over (h)}_(j)(d))) over their runtimes.

At least one embodiment of the invention includes generating wearindicator models by performing regression tasks with differentlydesigned daily hazard setups (that is, different α and β values), anddetermining the optimal wear indicator model in terms of the economicoptimization criterion estimate by leave-one-component-outcross-validations. Such wear indicator model generation is described infurther detail below.

Given an identification of previously replaced components (failure orscheduled replacements) and currently running components (as yet to bereplaced) for a component type over a group or fleet of vehicles, aswell as the corresponding time-stamped logs of runtime hours (meter),total fuel consumption, total work (load) and sensor events, at leastone embodiment of the invention includes generating a wear indicator forthe component type using regression techniques.

By way of illustration, suppose that there are a total of J componentsthat were previously replaced or are actively running (as yet to bereplaced) for the target component type. For component j (=1, . . . ,J), the start date of service is T_(S)(j), and the final date ofobservation is T_(F)(j). Note that the final date of observation isdefined as the replaced date for past components and the last observeddate for actively running components (as yet to be replaced). For thistask, the overall data set includes all points x(j,d) over component j(=1, . . . , J) and date d (=T_(S)(j), . . . , T_(F)(j)). Accordingly,input data, from the start date of service of component j, can includethe following:

Meter(j,d)=accumulated runtime hours over days up to and including dated;

Fuel(j,d)=accumulated fuel consumption over days up to and includingdate d;

Load(j,d)=accumulated number of loads (that is, total work) over days upto and including date d; and

EventCount(j,d)=accumulated number of relevant sensor events for thetarget component type over days up to and including date d. Such“relevant sensor events” can include, for example, an engine componentbeing connected to sensor events such as engine overheating,over-speeding, etc.

Note that, in an example embodiment of the invention, Meter(j,T_(S)(j))=0, Fuel(j, T_(S)(j))=0, Load(j, T_(S)(j))=0, and EventCount(j,T_(S)(j))=0. Additionally, in one or more embodiments of the invention,the relevant sensor event types for the component type can be selectedusing the significance test in a univariate Cox proportional hazardmodel for each event type. It is to be appreciated by one skilled in theart, however, that one or more embodiments of the invention canencompass and/or implement other techniques such as frequent sequencesearching on component failure.

Further, given the parameters such as (i) N_(smooth)=positive integerfor a smoothing filter, (ii) N_(fuel)=positive real threshold value forcounting the number of dates with a high daily fuel rate, and (iii)N_(load)=positive real threshold value for counting the number of dateswith a high daily load rate, at least one embodiment of the inventionincludes computing intermediate variables as detailed below. TheN_(smooth) parameter is used to compute a smoothed value, which can alsobe referred to as a moving average. For example, as detailed below, in“the average daily meter hours over the past N_(smooth) days on date d,”the particular “average daily meter hours” value depends on the givendate d.

Note that the intermediate variables are used to calculate features.Also, note that a purpose of N_(fuel) and N_(load) is to count outliers,and while a rule-based outlier detection embodiment is detailed herein,it is to be appreciated by one skilled in the art that embodiments ofthe invention include a framework for incorporating and/or implementingother anomaly detection algorithms to be applied for effective featuregeneration.

As such, at least one embodiment of the invention includes computingintermediate variables as follows:

DailyMeter(j,d)=the daily meter hours on date d, also represented asMeter(j,d)−Meter(j,d−1);

DailyFuel(j,d)=the daily fuel consumption on date d, also represented asFuel(j,d)−Fuel(j,d−1);

DailyLoad(j,d)=the daily number of loads on date d, also represented asLoad(j,d)−Load(j,d−1);

SmoothedDailyMeter(j,d)=the average daily meter hours over the pastN_(smooth) days on date d;

SmoothedDailyFuel(j,d)=the average daily fuel consumption over the pastN_(smooth) days on date d;

SmoothedDailyLoad(j,d)=the average number of loads over the pastN_(smooth) days on date d;

DailyFuelRate(j,d)=SmoothedDailyFuel(j,d)/SmoothedDailyMeter(j,d);

DailyLoadRate(j,d)=SmoothedDailyLoad(j,d)/SmoothedDailyMeter(j,d);

HighFuelRateCount(j,d)=the accumulated count of days in which the dailyfuel rate>N_(fuel) over days up to and including date d; and

HighLoadRateCount(j,d)=the accumulated count of days in which the dailyload rate>N_(load) over days up to and including date d.

Before performing the regression task, at least one embodiment of theinvention includes performing a classification task to estimate theprobability of having the component failure within the next M runtimehours from each date d (that is, the date of each sample). Thisestimated failure probability can be used as a predictor variable in theregression task. Additionally, it is noted that this failure probabilitywould improve fitting to the designed daily hazard in the regressiontask as compared to a fitting without the failure probability variable.

In connection with the aforementioned classification task, at least oneembodiment of the invention includes computing features and assigninglabels to each sample data point x(j,d), as additionally explainedbelow, to model the predicted failure probability. By way of example,features for the classification task can include the following:

HighFuelRateCountPerMeter(j,d)=HighFuelRateCount(j,d)/Meter(j,d);

HighLoadRateCountPerMeter(j,d)=HighLoadRateCount(j,d)/Meter(j,d);

TotalFuelRate(j,d)=Fuel(j,d)/Meter(j,d);

TotalLoadRate(j,d)=Load(j,d)/Meter(j,d); and

TotalEventRate(j,d)=EventCount(j,d)/Meter(j,d).

Additionally, as noted above, one or more embodiments of the inventioninclude assigning the classification label L(j,d) to each point x(j,d)that corresponds to date d for component j. Note that, as used herein,x(j,d) is a multi-dimensional vector of classification features.Historical data of component replacements include multiple types ofreplacements on the final date of observation, wherein such types caninclude (i) scheduled replacement and (ii) in-field failure replacement.The goal of the classification task is to estimate the failureprobability within the next M runtime hours from each date d.Accordingly, at least one embodiment of the invention, implementingbinary classification labels of Failure and No Failure (or non-failure)classes, includes the following labeling scheme (referred to below asApproach1):

For a point x(j,d) on a failure-replaced component j, when Meter(j, d)is within M meter hours of the failure replacement (that is,Meter(j,d)>Meter(j, T_(F)(j))−M), classification label L(j,d) isassigned a Failure class; otherwise, classification label L(j,d) isassigned a No Failure class;

For any point x(j,d) on a schedule-replaced component j, classificationlabel L(j,d) is assigned a No Failure class; and

For any point x(j,d) on running component j, classification label L(j,d)is assigned a No Failure class.

In addition to this labeling scheme, alternatively, at least oneembodiment of the invention includes implementing another labelingscheme (referred to below as Approach2), as follows:

For a point x(j, d) from a component j of any replacement (that is,regardless of failure or scheduled replacement), when Meter(j,d) iswithin M meter hours of the replacement (that is, Meter(j,d)>Runtime(j,T_(F)(j))−M), classification label L(j,d) is assigned a Failure class;otherwise, classification label L(j, d) is assigned a No Failure class;and

For point x(j, d) from currently active (that is, right-censored)component j, classification label L(j, d) is assigned a No Failureclass.

An underlying assumption of Approach2, for example, is that scheduledreplacement components in the data set would have failed very soon ifthey had not been replaced at the scheduled replacement runtime hours.

Further, for each component with a scheduled replacement, Approach1assigns a “No Failure” class to all sample points and a “Failure” classto none; and Approach2 assigns a “Failure” class to all sample pointswithin a pre-specified number (M) of meter hours before a scheduledreplacement and a “No Failure” class to all sample points preceding theFailure class.

At least one embodiment of the invention includes testing both labelingschemes and selecting the scheme that generates a better cumulativewear-based indicator in terms of the optimization criterion such as theaverage maintenance cost per unit runtime. To measure the performance ofan example embodiment of the invention, a leave-one-component-out crossvalidation can be carried out. That is, for each run corresponding to acomponent j (=1, . . . , J), the overall data set is split into (i) atest data set of all points from component j and (ii) a training dataset of all points from all J−1 remaining components k (≠j).Additionally, such an embodiment includes generating a wear indicatormodel based on the training data set only, and computing the wearindicator values on all points in the test data set.

By way of illustration, consider an example embodiment of the invention,wherein the initial parameters include α and β (designing dailyhazards), N_(smooth), N_(fuel), N_(load) (computing features), and M(modeling failure probability). Further, in such an example embodiment,if there are J runs in total, and in each run corresponding to acomponent j, the following steps are performed:

Step 1: Divide the overall data set into (i) the test data set of allpoints from one component j and (ii) the training data set of all pointsfrom remaining components.

Step 2: Using only the training data set, perform the classification tobuild a binary classifier (for example, via applying support vectorclassification) to compute the to failure probability P_(failure)(j, d)(that is, the probability of being a Failure class) on each point. Thisestimated probability can be viewed as the failure probability withinthe next M runtime hours from date d.

Step 3: Design the target variable for the regression task, wherein theregression target variable {tilde over (h)}_(k)(d) for any component k(≠j) in the training data set should have the desired characteristic ofthe daily hazard such as being monotonically increasing, convex-shaped,and the maximum value on failure.

Step 4: Using only the training data set, generate the regression model(for example, via applying support vector regression) to target thedaily hazard {tilde over (h)}_(k)(d) with feature variables such asMeter(k,d), Fuel(k,d), Load(k, d), EventCount(k,d) and P_(failure)(j,d).

Step 5: Apply the generated regression model to each point x(j,d) oncomponent j in the testing data set to obtain the estimated daily hazardh_(j)(d) for each point x(j,d) on component j in the testing data set.

Step 6: Compute the individualized cumulative hazard on component j viaH_(j)(t)=Σ_(all d in{d:Meter(j,d)≦t})h_(j)(d).

Step 7: Compute the individualized cumulative failure probability oncomponent j via F_(j)(t)=1−exp(−H_(j)(t)).

After all J runs in leave-one-component-out cross validations, the wearindicator values (that is, the individualized cumulative failureprobability (F) as output from Step 7) over all components can bedetermined. Given these values, at least one embodiment of the inventionincludes performing an optimization task to identify the optimalthreshold value for the replacement policy in terms of an economicoptimization criterion such as, for example, the average maintenancecost per unit runtime. Note that in a threshold-based replacementpolicy, a component should be replaced when the wear indicator valuereaches a threshold value. Optionally, one or more embodiments of theinvention can include using the estimated optimal threshold value tonormalize the wear indicator. In such an instance, a component should bereplaced when its wear indicator value is 100% of wear.

As detailed herein, parameter selections (α, β, N_(smooth), N_(fuel),N_(load), M) and the choice of the labeling scheme for estimatingfailure probability on the classification task influence the obtainedwear indicator model. Accordingly, an aspect of the invention includesdetermining the optimal parameters to obtain the best wear indicatormodel in terms of a given optimization criterion.

FIG. 1 is a diagram illustrating system architecture, according to anexample embodiment of the present invention. By way of illustration,FIG. 1 depicts a wear-based indicator generation system 110, whichreceives input from sensors 102A, 102B and 102C resident on and/orconnected to vehicles 101A, 101B and 101C, respectively. By way merelyof example, the input from sensors 102A, 102B and 102C can betransmitted wirelessly to the system 110 and/or can be transmitted tothe system 110 via a direct electrical connection (for instance, viacreating an electrical connection or interface between a given sensorand the system 110 upon detaching the sensor from a given vehicle).Additionally, the system 110 also receives input from a componentreplacement database 106, as further described herein.

As illustrated in FIG. 1, the wear-based indicator generation system 110includes a classification engine 112, a failure probability estimationengine 114, a cumulative hazard function determination engine 116, acumulative wear-based indicator generator engine 118, a graphical userinterface 120 and a display 122. As further detailed herein, engines112, 114, 116 and 118 process multiple forms of data to generate acumulative wear-based indicator for one or more given vehicularcomponents based on the input provided by sensors 102A, 102B and 102C aswell as from database 104. The generated cumulative wear-based indicatorfor the given vehicular components are then transmitted to the graphicaluser interface 120 and the display 122 for presentation and/or potentialmanipulation by a user.

FIG. 2 is a flow diagram illustrating techniques according to anembodiment of the present invention. Step 202 includes assigning afailure class label to each data point, from a set of multiple datapoints derived from measurements associated with a vehicular componentacross a fleet of multiple vehicles, that (a) is associated with (i) ascheduled vehicular component replacement or (ii) a failure-causedvehicular component replacement, and (b) is within a pre-specifiednumber of runtime hours of (i) the scheduled vehicular componentreplacement or (ii) the failure-caused vehicular component replacement.

Step 204 includes assigning a non-failure class label to each datapoint, from the set of the multiple data points, that (a) is associatedwith (i) a scheduled vehicular component replacement or (ii) afailure-caused vehicular component replacement, and (b) is not withinthe pre-specified number of runtime hours of (i) the scheduled vehicularcomponent replacement or (ii) the failure-caused vehicular componentreplacement. Step 206 includes assigning a non-failure class label toeach data point, from the set of the multiple data points, that isassociated with an actively running instance of the vehicular componentas yet to be replaced.

Step 208 includes estimating a failure probability for the vehicularcomponent at each of the multiple data points over a pre-specifiedfuture runtime of the vehicular component based on the class labelassigned to each of the multiple data points. Techniques that can beused to carry out this estimation step can include, for example, supportvector classification (SVC) techniques and/or support vector regression(SVR) techniques.

Step 210 includes determining a cumulative hazard function for thevehicular component based on the failure probability, wherein saidcumulative hazard function assesses the amount of accumulated risk thatthe vehicular component faced from a given start time until the presenttime. The failure probability (F_(j)(t) for the vehicular componentrelates to the cumulative hazard function (H_(j)(t)) for the vehicularcomponent such that F_(j)(t)=1−S_(j)(t)=1−exp(−H_(j)(t)) whereinS_(j)(t) is a survival probability function for the vehicular componentj at time t.

Additionally, in at least one embodiment of the invention, thecumulative hazard function is based on an aggregate of multiple hazardfunction values of a given temporal interval across a given timeframe.By way of example, the given temporal interval can be one day, and insuch an embodiment of the invention, each of the multiple hazardfunctions of a one day temporal interval is defined as the total hazard(h_(j)(d)) during the daily runtime on day d for vehicular component j.Also, in such an embodiment, the aggregate (H_(j)(t)) of multiple hazardfunctions of a one day temporal interval across the given timeframecomprises H_(j)(t)=Σ_(all d in{d:Meter(j,d)≦t})h_(j)(d), whereinMeter(j,d) represents the accumulated runtime hours over days up to andincluding date d, and wherein the given timeframe comprises a givenstart date through time t.

Step 212 includes generating a cumulative wear-based indicator for thevehicular component by executing a regression function at a given timebased on (i) the cumulative hazard function, (ii) one or more selectedparameters, and (iii) a determination as to whether the vehicularcomponent (a) was previously replaced due to a failure, (b) waspreviously replaced due to a non-failure scheduled replacement, or (c)is actively running as yet to be replaced. The selected parameters caninclude (i) the accumulated fuel consumption over a given time period,(ii) the accumulated amount of work over the given time period, and/or(iii) the accumulated number of sensor events for a target componenttype that encompasses the vehicular component over the given timeperiod. It is also to be appreciated by one skilled in the art that oneor more additional parameters can be encompassed by one or moreembodiments of the invention.

The given time can include a given date, wherein said vehicularcomponent was previously replaced due to a failure, and wherein saidexecuting the regression function ({tilde over (h)}_(j)(d)) comprisescalculating {tilde over (h)}_(j)(d)=(Meter(j,d)/Meter(j,T_(F)(j)))^(α),wherein Meter(j,d) represents the total number of runtime hours up toand including date d, T_(F)(j) is the date that the vehicular componentwas previously replaced due to a failure, and α≧1. Additionally, thegiven time can include a given date, wherein said vehicular componentwas previously replaced due to a non-failure scheduled replacement, andwherein said executing the regression function ({tilde over (h)}_(j)(d))includes calculating {tilde over (h)}_(j)(d)=β(Meter(j,d)/M_(max))^(α),wherein M_(max)=max_(i)[Meter(i, T_(F)(i))], which represents themaximum total number of runtime hours over all vehicular components in agiven data set (for instance, the set of multiple data points), and βrepresents a positive number between zero and one. Further, the giventime can include a given date, wherein said vehicular component isactively running as yet to be replaced, and wherein said executing theregression function ({tilde over (h)}_(j)(d)) includes calculating{tilde over (h)}_(j)(d)−β(Meter(j,d)/M_(max))^(α), whereinM_(max)=max_(i)[Meter(i, T_(F)(i))], which represents the maximum totalnumber of runtime hours over all vehicular components in a given dataset, and β represents a positive number between zero and one.

The techniques depicted in FIG. 2 can also include generating multiplecumulative wear-based indicators for the vehicular component byexecuting multiple regression functions, wherein each of the multipleregression functions comprises a distinct combination of the one or moreselected parameters. Additionally, the techniques depicted in FIG. 2 canfurther include identifying the cumulative wear-based indicator from themultiple cumulative wear-based indicators that optimizes a givencriterion.

Also, the techniques depicted in FIG. 2 can include obtaining at leastone input time series pertaining to the vehicular component across thefleet of vehicles, wherein each input time series includes data pointsfrom the set of multiple data points derived from the measurementsassociated with the vehicular component across the fleet of multiplevehicles.

FIG. 3 is a flow diagram illustrating techniques according to anembodiment of the invention. Step 302 includes assigning a failure classlabel to each data point, from a set of multiple data points derivedfrom measurements associated with a vehicular component across a fleetof multiple vehicles, that (a) is associated with a failure-causedvehicular component replacement, and (b) is within a pre-specifiednumber of runtime hours of the failure-caused vehicular componentreplacement. Step 304 includes assigning a non-failure class label toeach data point, from the set of the multiple data points, that (a) isassociated with a failure-caused vehicular component replacement, and(b) is not within the pre-specified number of runtime hours of thefailure-caused vehicular component replacement. Step 306 includesassigning a non-failure class label to each data point, from the set ofthe multiple data points, that is associated with a scheduled vehicularcomponent replacement. Step 308 includes assigning a non-failure classlabel to each data point, from the set of the multiple data points, thatis associated with an actively running instance of the vehicularcomponent as yet to be replaced.

Step 310 includes estimating a failure probability for the vehicularcomponent at each of the multiple data points over a pre-specifiedfuture runtime of the vehicular component based on the class labelassigned to each of the multiple data points. Step 312 includesdetermining a cumulative hazard function for the vehicular componentbased on the failure probability, wherein said cumulative hazardfunction assesses the amount of accumulated risk that the vehicularcomponent has faced from a given start time until the present time. Step314 includes generating a cumulative wear-based indicator for thevehicular component by executing a regression function at a given timebased on (i) the cumulative hazard function, (ii) one or more selectedparameters, and (iii) a determination as to whether the vehicularcomponent (a) was previously replaced due to a failure, (b) waspreviously replaced due to a non-failure scheduled replacement, or (c)is actively running as yet to be replaced.

The techniques depicted in FIG. 2 and FIG. 3 can also, as describedherein, include providing a system, wherein the system includes distinctsoftware modules, each of the distinct software modules being embodiedon a tangible computer-readable recordable storage medium. All of themodules (or any subset thereof) can be on the same medium, or each canbe on a different medium, for example. The modules can include any orall of the components shown in the figures and/or described herein. Inan aspect of the invention, the modules can run, for example, on ahardware processor. The method steps can then be carried out using thedistinct software modules of the system, as described above, executingon a hardware processor. Further, a computer program product can includea tangible computer-readable recordable storage medium with code adaptedto be executed to carry out at least one method step described herein,including the provision of the system with the distinct softwaremodules.

Additionally, the techniques depicted in FIG. 2 and FIG. 3 can beimplemented via a computer program product that can include computeruseable program code that is stored in a computer readable storagemedium in a data processing system, and wherein the computer useableprogram code was downloaded over a network from a remote data processingsystem. Also, in an aspect of the invention, the computer programproduct can include computer useable program code that is stored in acomputer readable storage medium in a server data processing system, andwherein the computer useable program code is downloaded over a networkto a remote data processing system for use in a computer readablestorage medium with the remote system.

An aspect of the invention or elements thereof can be implemented in theform of an apparatus including a memory and at least one processor thatis coupled to the memory and configured to perform exemplary methodsteps.

Additionally, an aspect of the present invention can make use ofsoftware running on a general purpose computer or workstation. Withreference to FIG. 4, such an implementation might employ, for example, aprocessor 402, a memory 404, and an input/output interface formed, forexample, by a display 406 and a keyboard 408. The term “processor” asused herein is intended to include any processing device, such as, forexample, one that includes a CPU (central processing unit) and/or otherforms of processing circuitry. Further, the term “processor” may referto more than one individual processor. The term “memory” is intended toinclude memory associated with a processor or CPU, such as, for example,RAM (random access memory), ROM (read only memory), a fixed memorydevice (for example, hard drive), a removable memory device (forexample, diskette), a flash memory and the like. In addition, the phrase“input/output interface” as used herein, is intended to include, forexample, a mechanism for inputting data to the processing unit (forexample, mouse), and a mechanism for providing results associated withthe processing unit (for example, printer). The processor 402, memory404, and input/output interface such as display 406 and keyboard 408 canbe interconnected, for example, via bus 410 as part of a data processingunit 412. Suitable interconnections, for example via bus 410, can alsobe provided to a network interface 414, such as a network card, whichcan be provided to interface with a computer network, and to a mediainterface 416, such as a diskette or CD-ROM drive, which can be providedto interface with media 418.

Accordingly, computer software including instructions or code forperforming the methodologies of the invention, as described herein, maybe stored in associated memory devices (for example, ROM, fixed orremovable memory) and, when ready to be utilized, loaded in part or inwhole (for example, into RAM) and implemented by a CPU. Such softwarecould include, but is not limited to, firmware, resident software,microcode, and the like.

A data processing system suitable for storing and/or executing programcode will include at least one processor 402 coupled directly orindirectly to memory elements 404 through a system bus 410. The memoryelements can include local memory employed during actual implementationof the program code, bulk storage, and cache memories which providetemporary storage of at least some program code in order to reduce thenumber of times code must be retrieved from bulk storage duringimplementation.

Input/output or I/O devices (including but not limited to keyboards 408,displays 406, pointing devices, and the like) can be coupled to thesystem either directly (such as via bus 410) or through intervening I/Ocontrollers (omitted for clarity).

Network adapters such as network interface 414 may also be coupled tothe system to enable the data processing system to become coupled toother data processing systems or remote printers or storage devicesthrough intervening private or public networks. Modems, cable modems andEthernet cards are just a few of the currently available types ofnetwork adapters.

As used herein, including the claims, a “server” includes a physicaldata processing system (for example, system 412 as shown in FIG. 4)running a server program. It will be understood that such a physicalserver may or may not include a display and keyboard.

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as a system, method and/or computer programproduct. Accordingly, aspects of the present invention may take the formof an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, as noted herein, aspects of the present invention may takethe form of a computer program product that may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (for example, lightpulses passing through a fiber-optic cable), or electrical signalstransmitted through a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Java, Smalltalk, C++ or the like,and conventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

It should be noted that any of the methods described herein can includean additional step of providing a system comprising distinct softwaremodules embodied on a computer readable storage medium; the modules caninclude, for example, any or all of the components detailed herein. Themethod steps can then be carried out using the distinct software modulesand/or sub-modules of the system, as described above, executing on ahardware processor 402. Further, a computer program product can includea computer-readable storage medium with code adapted to be implementedto carry out at least one method step described herein, including theprovision of the system with the distinct software modules.

In any case, it should be understood that the components illustratedherein may be implemented in various forms of hardware, software, orcombinations thereof, for example, application specific integratedcircuit(s) (ASICS), functional circuitry, an appropriately programmedgeneral purpose digital computer with associated memory, and the like.Given the teachings of the invention provided herein, one of ordinaryskill in the related art will be able to contemplate otherimplementations of the components of the invention.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a,” “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition ofanother feature, integer, step, operation, element, component, and/orgroup thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed.

At least one aspect of the present invention may provide a beneficialeffect such as, for example, generating a non-decreasing cumulative wearindicator function for a given vehicular component that is a function ofan input time series corresponding to the component.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

What is claimed is:
 1. A method comprising the following steps:assigning a failure class label to each data point, from a set ofmultiple data points derived from measurements associated with avehicular component across a fleet of multiple vehicles, that (a) isassociated with a failure-caused vehicular component replacement, and(b) is within a pre-specified number of runtime hours of thefailure-caused vehicular component replacement; assigning a non-failureclass label to each data point, from the set of the multiple lo datapoints, that (a) is associated with a failure-caused vehicular componentreplacement, and (b) is not within the pre-specified number of runtimehours of the failure-caused vehicular component replacement; assigning anon-failure class label to each data point, from the set of the multipledata points, that is associated with a scheduled vehicular componentreplacement; assigning a non-failure class label to each data point,from the set of the multiple data points, that is associated with anactively running instance of the vehicular component as yet to bereplaced; estimating a failure probability for the vehicular componentat each of the multiple data points over a pre-specified future runtimeof the vehicular component based on the class label assigned to each ofthe multiple data points; determining a cumulative hazard function forthe vehicular component based on the failure probability, wherein saidcumulative hazard function assesses the amount of accumulated risk thatthe vehicular component has faced from a given start time until thepresent time; and generating a cumulative wear-based indicator for thevehicular component by executing a regression function at a given timebased on (i) the cumulative hazard function, (ii) one or more selectedparameters, and (iii) a determination as to whether the vehicularcomponent (a) was previously replaced due to a failure, (b) waspreviously replaced due to a non-failure scheduled replacement, or (c)is actively running as yet to be replaced; wherein at least one of thesteps is carried out by a computing device.
 2. The method of claim 1,comprising: obtaining at least one input time series pertaining to thevehicular component across the fleet of multiple vehicles, wherein eachinput time series comprises data points from the set of multiple datapoints derived from the measurements associated with the vehicularcomponent across the fleet of multiple vehicles.
 3. The method of claim1, wherein said failure probability (F_(j)(t)) for the vehicularcomponent relates to said cumulative hazard function (H_(j)(t)) for thevehicular component such that F_(j)(t)=1−S_(j)(t)=1−exp(−H_(j)(t))wherein S_(j)(t) is a survival probability function for the vehicularcomponent j at time t.
 4. The method of claim 1, wherein said cumulativehazard function is based on an aggregate of multiple hazard functionvalues of a given temporal interval across a given timeframe.
 5. Themethod of claim 4, wherein said given temporal interval is one day, andwherein each of said multiple hazard functions of a one day temporalinterval is defined as the total hazard (h_(j)(d)) during the dailyruntime on day d for vehicular component j.
 6. The method of claim 5,wherein the aggregate (H_(j)(t)) of multiple hazard functions of a oneday temporal interval across the given timeframe comprisesH_(j)(t)=Σ_(all d in{d:Meter(j,d)≦t})h_(j)(d), wherein Meter(j,d)represents the accumulated runtime hours over days up to and includingdate d, and wherein the given timeframe comprises a given start datethrough time t.
 7. The method of claim 1, wherein said given timecomprises a given date, wherein said vehicular component was previouslyreplaced due to a failure, and wherein said executing the regressionfunction ({tilde over (h)}_(j)(d)) comprises calculating {tilde over(h)}_(j)(d)=(Meter(j,d)/Meter(j,T_(F)(j)))^(α), wherein Meter(j,d)represents the total number of runtime hours up to and including date d,T_(F)(j) is the date that the vehicular component was previouslyreplaced due to a failure, and α≧1.
 8. The method of claim 1, whereinsaid given time comprises a given date, wherein said vehicular componentwas previously replaced due to a non-failure scheduled replacement, andwherein said executing the regression function ({tilde over (h)}_(j)(d))comprises calculating {tilde over (h)}_(j)(d)=β(Meter(j,d)/M_(max))^(α),wherein M_(max)=max_(i)[Meter(i, T_(F)(i))], which represents themaximum total number of runtime hours over all vehicular components inthe set of multiple data points, and β represents a positive numberbetween zero and one.
 9. The method of claim 1, wherein said given timecomprises a given date, wherein said vehicular component is activelyrunning as yet to be replaced, and wherein said executing the regressionfunction ({tilde over (h)}_(j)(d)) comprises calculating {tilde over(h)}_(j)(d)=β(Meter(j,d)/M_(max))^(α), wherein M_(max)=max_(i)[Meter(i,T_(F)(i))], which represents the maximum total number of runtime hoursover all vehicular components in the set of multiple data points, and 0represents a positive number between zero and one.
 10. The method ofclaim 1, wherein the one or more selected parameters comprise (i) theaccumulated fuel consumption over a given time period, (ii) theaccumulated amount of work over the given time period, and/or (iii) theaccumulated number of sensor events for a target component type thatencompasses the vehicular component over the given time period.
 11. Themethod of claim 1, comprising: generating multiple cumulative wear-basedindicators for the vehicular component by executing multiple regressionfunctions, wherein each of the multiple regression functions comprises adistinct combination of the one or more selected parameters; andidentifying the cumulative wear-based indicator from the multiplecumulative wear-based indicators that optimizes a given criterion.
 12. Acomputer program product, the computer program product comprising acomputer readable storage medium having program instructions embodiedtherewith, the program instructions executable by a computing device tocause the computing device to: assign a failure class label to each datapoint, from a set of multiple data points derived from measurementsassociated with a vehicular component across a fleet of multiplevehicles, that (a) is associated with a failure-caused vehicularcomponent replacement, and (b) is within a pre-specified number ofruntime hours of the failure-caused vehicular component replacement;assign a non-failure class label to each data point, from the set of themultiple data points, that (a) is associated with a failure-causedvehicular component replacement, and (b) is not within the pre-specifiednumber of runtime hours of the failure-caused vehicular componentreplacement; assign a non-failure class label to each data point, fromthe set of the multiple data points, that is associated with a scheduledvehicular component replacement; assign a non-failure class label toeach data point, from the set of the multiple data points, that isassociated with an actively running instance of the vehicular componentas yet to be replaced; estimate a failure probability for the vehicularcomponent at each of the multiple data points over a pre-specifiedfuture runtime of the vehicular component based on the class labelassigned to each of the multiple data points; determine a cumulativehazard function for the vehicular component based on the failureprobability, wherein said cumulative hazard function assesses the amountof accumulated risk that the vehicular component has faced from a givenstart time until the present time; and generate a cumulative wear-basedindicator for the vehicular component by executing a regression functionat a given time based on (i) the cumulative hazard function, (ii) one ormore selected parameters, and (iii) a determination as to whether thevehicular component (a) was previously replaced due to a failure, (b)was previously replaced due to a non-failure scheduled replacement, or(c) is actively running as yet to be replaced.
 13. The computer programproduct of claim 12, wherein said failure probability (F_(j)(t)) for thevehicular component relates to said cumulative hazard function(H_(j)(t)) for the vehicular component such thatF_(j)(t)=1−S_(j)(t)=1−exp(−H_(j)(t)) wherein S_(j)(t) is a survivalprobability function for the vehicular component j at time t.
 14. Thecomputer program product of claim 12, wherein said cumulative hazardfunction is based on an aggregate of multiple hazard function values ofa given temporal interval across a given timeframe.
 15. The computerprogram product of claim 14, wherein said given temporal interval is oneday, and wherein each of said multiple hazard functions of a one daytemporal interval is defined as the total hazard (h_(j)(d)) during thedaily runtime on day d for vehicular component j.
 16. The computerprogram product of claim 15, wherein the aggregate (H_(j)(t)) ofmultiple hazard functions of a one day temporal interval across thegiven timeframe comprises H_(j)(t)=Σ_(all d in{d:Meter(j,d)≦t})h_(j)(d),wherein Meter(j, d) represents the accumulated runtime hours over daysup to and including date d, and wherein the given timeframe comprises agiven start date through time t.
 17. The computer program product ofclaim 12, wherein said given time comprises a given date, wherein saidvehicular component was previously replaced due to a failure, andwherein said executing the regression function ({tilde over (h)}_(j)(d))comprises calculating {tilde over (h)}_(j)(d)=(Meter(j,d)/Meter(j,T_(F)(j)))^(α), wherein Meter(j,d) represents the total number ofruntime hours up to and including date d, T_(F)(j) is the date that thevehicular component was previously replaced due to a failure, and α≧1.18. The computer program product of claim 12, wherein said given timecomprises a given date, wherein said vehicular component was previouslyreplaced due to a non-failure scheduled replacement, and wherein saidexecuting the regression function ({tilde over (h)}_(j)(d)) comprisescalculating {tilde over (h)}_(j)(d)=β(Meter(j,d)/M_(max))^(α), whereinM_(max)=max_(i)[Meter(i,T_(F)(i))], which represents the maximum totalnumber of runtime hours over all vehicular components in the set ofmultiple data points, and β represents a positive number between zeroand one.
 19. The computer program product of claim 12, wherein saidgiven time comprises a given date, wherein said vehicular component isactively running as yet to be replaced, and wherein said executing theregression function ({tilde over (h)}(d)) comprises calculating {tildeover (h)}_(j)=β(Meter(j,d)/M_(max))^(α), whereinM_(max)=max_(i)[Meter(i, T_(F)(i))], which represents the maximum totalnumber of runtime hours over all vehicular components in the set ofmultiple data points, and β represents a positive number between zeroand one.
 20. The computer program product of claim 12, wherein the oneor more selected parameters comprise (i) the accumulated fuelconsumption over a given time period, (ii) the accumulated amount ofwork over the given time period, and/or (iii) the accumulated number ofsensor events for a target component type that encompasses the vehicularcomponent over the given time period.